Author:
Green Nathan,Ngo Dac Tuan
Abstract
Abstract
In 2007 Chang and Yu determined all the algebraic relations among Goss’s zeta values for
$A=\mathbb F_q[\theta ]$
, also known as the Carlitz zeta values. Goss raised the problem of determining all algebraic relations among Goss’s zeta values at positive integers for a general base ring A, but very little is known. In this paper, we develop a general method, and we determine all algebraic relations among Goss’s zeta values for the base ring A which is the coordinate ring of an elliptic curve defined over
$\mathbb F_q$
. To our knowledge, this is the first work tackling Goss’s problem when the base ring has class number strictly greater than 1.
Publisher
Cambridge University Press (CUP)
Subject
Computational Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science,Analysis
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